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We consider an interval $D=[-\\pi,\\pi]$ under periodic boundary condition where $\\dot{W}(t,x)$ is a space-time white noise and $\\sigma(u)\\approx u^{\\gamma}$ near $\\infty$. Our results refine existing results by identifying behavior in a previously less understood regime, where we show that if $\\beta\\in(1,3),\\gamma\\in(\\frac{\\beta}{2},\\frac{\\beta+3}{4})$ or $\\beta>1,\\gamma\\in(0,\\frac{\\beta}{2}]$ then m","authors_text":"Michael Salins, Yuyang Zhang","cross_cats":[],"headline":"Mild solutions to the stochastic heat equation explode with positive probability for beta in (1,3) with gamma in (beta/2, (beta+3)/4) or beta greater than 1 with gamma up to beta/2.","license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-05-11T23:11:52Z","title":"Positive probability of explosion for stochastic heat equation with superlinear accretive reaction term and polynomially growing multiplicative noise"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"2605.11319","kind":"arxiv","version":2},"verdict":{"created_at":"2026-05-13T01:34:50.623194Z","id":"7fdc838f-507c-4392-8af4-4c0c527139d5","model_set":{"reader":"grok-4.3"},"one_line_summary":"Mild solutions explode with positive probability when β ∈ (1,3) and γ ∈ (β/2, (β+3)/4), or when β > 1 and γ ∈ (0, β/2].","pipeline_version":"pith-pipeline@v0.9.0","pith_extraction_headline":"Mild solutions to the stochastic heat equation explode with positive probability for beta in (1,3) with gamma in (beta/2, (beta+3)/4) or beta greater than 1 with gamma up to beta/2.","strongest_claim":"if β∈(1,3),γ∈(β/2,(β+3)/4) or β>1,γ∈(0,β/2] then mild solutions can explode with positive probability.","weakest_assumption":"The assumption that σ(u) ≈ u^γ near infinity together with the existence of mild solutions up to the potential explosion time on the periodic interval."}},"verdict_id":"7fdc838f-507c-4392-8af4-4c0c527139d5"}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:990c47c5807c70a760bcb5aa266beba08d7585ae4b0af0212e1fe483b4aadec7","target":"record","created_at":"2026-05-29T02:05:46Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"83b2e441061d025f19a6db595da43bcc10c9c6910b332c6e9cf4bef32ebcfd01","cross_cats_sorted":[],"license":"http://creativecommons.org/licenses/by/4.0/","primary_cat":"math.PR","submitted_at":"2026-05-11T23:11:52Z","title_canon_sha256":"0e18dbef41f1664e5f4e380e554175ca9b1b6d7ff47e5c6605187c30b7472989"},"schema_version":"1.0","source":{"id":"2605.11319","kind":"arxiv","version":2}},"canonical_sha256":"eb32e2d183531160a1aa97f385a96016415a11b5e8c70465bd3bb93b541c3c89","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"eb32e2d183531160a1aa97f385a96016415a11b5e8c70465bd3bb93b541c3c89","first_computed_at":"2026-05-29T02:05:46.475794Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-29T02:05:46.475794Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"AbYepAYlsuvz1YDdE61rASQ5GrNHCcnRv+AcHSZBbPvH+P5AX8Tvp6r3oI1x+VDByo4VDdxMbD7Fn6VmI63XCA==","signature_status":"signed_v1","signed_at":"2026-05-29T02:05:46.476568Z","signed_message":"canonical_sha256_bytes"},"source_id":"2605.11319","source_kind":"arxiv","source_version":2}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:990c47c5807c70a760bcb5aa266beba08d7585ae4b0af0212e1fe483b4aadec7","sha256:7b2ae9bb2602dd641381fac63f5efbfc7ae3fed3d51c3a3501a91e08b4d34155"],"state_sha256":"08ae14169bf166028ba6421f254e6e1f04e9b9e21f4c3e25e4270230aed44da0"}